Finite Group Databasebeta

← C13×#9516 #15695855

Subgroups — C13×#9516 #15695855

Order 3328.

626 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2975C211yesmaximal, characteristic, complemented
2C13×#2534C211yesmaximal, characteristic
3C13×#1465C211yesmaximal, characteristic, complemented
4C13×#1462C212yesmaximal, complemented
5C13×#1305C212yesmaximal, complemented
6C2×C13×#123C411yescharacteristic
7C2×C13×#120C411yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C13×#436—24no—
11C13×#431—21no—
12C13×#407—21no—
13C13×#407C2212yes—
14C13×#407C2212yes—
15C13×#396—21no—
16C13×#394—21no—
17C13×#388—21no—
18C13×#386—21no—
19C13×#381C411yescharacteristic
20C13×#380C2211yescharacteristic
21C13×#379C411yescharacteristic
22C13×#324—21no—
23C13×#323—21no—
24C13×#323—24no—
25C25×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C2×C13×M16—22no—
32C2×C13×M16—22no—
33C2×C13×M16—22no—
34C13×#123—42no—
35C13×#120—42no—
36C4×D4×C13—22no—
37C4×D4×C13—22no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4C2×C411yescharacteristic
51C2×C13×C22⋊C4C2×C411yescharacteristic
52C2×C13×C22⋊C4D411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C13×C4⋊C8—22no—
55C13×C22⋊C8—22no—
56C13×C22⋊C8—22no—
57C13×C22⋊C8—22no—
58C13×C22⋊C8—22no—
59C13×C22⋊C8D414yescomplemented
60C4×C8×C13—22no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#9516C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13—22no—
67C24×C13—42no—
68C24×C13—41no—
69C24×C13—41no—
70C24×C13—81no—
71C24×C13C22⋊C411yescharacteristic
72C24×C13C22×C411yescharacteristic
73C2×D4×C13—22no—
74C2×D4×C13—22no—
75C2×D4×C13—41no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—81no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—22no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—81no—
88C22×C4×C13—81no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C2×D412yes—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4112yes—
96C13×M16—82no—
97C13×M16—82no—
98C13×M16—82no—
99C2×C8×C13—24no—
100C2×C8×C13—42no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—81no—
115C42×C13—21no—
116C42×C13—21no—
117#2975C2×C1311yescharacteristic, complemented
118#2534C2×C1311yescharacteristic
119#1465C2×C1311yescharacteristic, complemented
120#1462C2×C1312yescomplemented
121#1305C2×C1312yescomplemented
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—22no—
125C23×C13—24no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—42no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—82no—
141C23×C13—82no—
142C23×C13—84no—
143C23×C13—84no—
144C23×C13C2×C22⋊C411yescharacteristic
145C23×C13C4×D412yes—
146D4×C13—44no—
147D4×C13—84no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—81no—
169C2×C4×C13—82no—
170C2×C4×C13#10012yes—
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12112yes—
173C2×C4×C13#12311yescharacteristic
174C8×C13—44no—
175C8×C13—82no—
176C2×#123C4×C1311yescharacteristic
177C2×#120C4×C1311yescharacteristic
178C2×C4×D4C22×C1311yescharacteristic
179C22×C22⋊C4C22×C1311yescharacteristic
180#436—24no—
181#431—21no—
182#407—21no—
183#407C22×C1312yes—
184#407C22×C1312yes—
185#396—21no—
186#394—21no—
187#388—21no—
188#386—21no—
189#381C4×C1311yescharacteristic
190#380C22×C1311yescharacteristic
191#379C4×C1311yescharacteristic
192#324—21no—
193#323—21no—
194#323—24no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—42no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—84no—
213C22×C13—84no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13#38611yescharacteristic
217C22×C13C2×#10011yescharacteristic
218C22×C13#41311yescharacteristic
219C4×C13—22no—
220C4×C13—21no—
221C4×C13—22no—
222C4×C13—21no—
223C4×C13—41no—
224C4×C13—41no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—81no—
228C25C2×C4×C1311yescharacteristic
229C22×D4—21no—
230C22×D4C2×C4×C1311yescharacteristic
231C23×C4C2×C4×C1311yescharacteristic
232C23×C4D4×C1311yescharacteristic
233C23×C4C23×C1311yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237#123—42no—
238#120—42no—
239C4×D4—22no—
240C4×D4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C1311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4C2×C4×C1311yescharacteristic
253C2×C22⋊C4C2×C4×C1311yescharacteristic
254C2×C22⋊C4C2×C4×C1311yescharacteristic
255C2×C22⋊C4D4×C1311yescharacteristic
256C2×C42D4×C1311yescharacteristic
257C4⋊C8—22no—
258C22⋊C8—22no—
259C22⋊C8—22no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8D4×C1314yescomplemented
263C4×C8—22no—
264#95—21no—
265#95—21no—
266#95—21no—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—42no—
270C2×C13—81no—
271C2×C13—82no—
272C2×C13#189111yescharacteristic
273C2×C13#190011yescharacteristic
274C2×C13#191311yescharacteristic
275C24—21no—
276C24—22no—
277C24—42no—
278C24—41no—
279C24—41no—
280C24—81no—
281C24C13×C22⋊C411yescharacteristic
282C24C22×C4×C1311yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—81no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4C13×C22⋊C411yescharacteristic
300C22×C4C13×C22⋊C411yescharacteristic
301C22×C4C13×C22⋊C411yescharacteristic
302C22×C4C2×D4×C1312yes—
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C13×#4112yes—
306M16—82no—
307M16—82no—
308M16—82no—
309C2×C8—24no—
310C2×C8—42no—
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—81no—
325C42—21no—
326C42—21no—
327C13#951611yescharacteristic, direct product factor, Sylow
328C23—21no—
329C23—21no—
330C23—22no—
331C23—24no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—42no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—82no—
347C23—82no—
348C23—84no—
349C23—84no—
350C23C2×C13×C22⋊C411yescharacteristic
351C23C4×D4×C1312yes—
352D4—44no—
353D4—84no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4C13×#10012yes—
377C2×C4C13×#12011yescharacteristic
378C2×C4C13×#12112yes—
379C2×C4C13×#12311yescharacteristic
380C8—44no—
381C8—82no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—84no—
400C22—84no—
401C22—81no—
402C22—81no—
403C22C13×#38611yescharacteristic
404C22C2×C13×#10011yescharacteristic
405C22C13×#41311yescharacteristic
406C4—22no—
407C4—21no—
408C4—22no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4—81no—
414C4—81no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—81no—
419C2—82no—
420C2C13×#189111yescharacteristic
421C2C13×#190011yescharacteristic
422C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC24C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#120C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#2975C2semidirect
3. C13×#1465C2semidirect
4. C13×#1462C2semidirect
5. C13×#1305C2semidirect
59. C13×C22⋊C8D4semidirect
64. #9516C13direct (N × H)
117. #2975C2×C13semidirect
119. #1465C2×C13semidirect
120. #1462C2×C13semidirect
121. #1305C2×C13semidirect
262. C22⋊C8D4×C13semidirect
327. C13#9516direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#29752
C13×#25342
C13×#14652
C13×#14622
C13×#13052
#951613